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A069811 a(n) = Sum_{k=1..n} omega(k)^2. 3
0, 1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 20, 21, 25, 29, 30, 31, 35, 36, 40, 44, 48, 49, 53, 54, 58, 59, 63, 64, 73, 74, 75, 79, 83, 87, 91, 92, 96, 100, 104, 105, 114, 115, 119, 123, 127, 128, 132, 133, 137, 141, 145, 146, 150, 154, 158, 162, 166, 167, 176, 177, 181 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fifth edition, Oxford University Press, Chap. XXII, p. 357.
LINKS
Paul Turán, On a theorem of Hardy and Ramanujan, Journal of the London Mathematical Society, Vol. s1-9, No. 4 (1934), pp. 274-276.
FORMULA
a(n) = Sum_{k=1..n} A001221(k)^2.
a(n) = n*log(log(n))^2 + O(n*log(log(n))) (Turán, 1934).
a(n) = Sum_{k>=1} k^2 * A346617(n,k). - Alois P. Heinz, Aug 19 2021
MATHEMATICA
Accumulate@((PrimeNu@Range@62)^2) (* Ivan Neretin, Mar 16 2017 *)
PROG
(PARI) a(n) = sum(k=1, n, omega(k)^2); \\ Michel Marcus, Mar 16 2017
CROSSREFS
Equals (A074787(n)-1)/4 for n <= 29.
Sequence in context: A061887 A005455 A047338 * A004826 A326783 A326785
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 30 2002
STATUS
approved

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Last modified February 29 04:20 EST 2024. Contains 370401 sequences. (Running on oeis4.)